log base 5 of 5
Understand the Problem
The question is asking for the logarithm of 5 to the base 5. This is a fundamental concept in logarithms, as it essentially asks what power 5 must be raised to in order to get 5, which is always 1. This problem is straightforward and requires basic knowledge of logarithmic properties.
Answer
$1$
Answer for screen readers
The final answer is $1$.
Steps to Solve
-
Identify the Logarithmic Expression
We need to evaluate the logarithmic expression $ \log_5{5} $. -
Apply the Logarithmic Property
By the definition of logarithms, we want to find the power to which the base (5) must be raised to get the number (5). This can be expressed as:
$$ x = \log_5{5} $$ -
Solve the Equation
We rewrite this equation in exponential form:
$$ 5^x = 5 $$
From this, we can see that $x$ must equal 1 since $5^1 = 5$. -
State the Result
Thus, we conclude that:
$$ \log_5{5} = 1 $$
The final answer is $1$.
More Information
This answer comes from the fundamental property of logarithms, where the logarithm of a number to its own base is always 1. This rule applies universally to any positive number where the base and the argument are the same.
Tips
- Misunderstanding the definition of logarithms can lead to confusion. It's important to remember that $ \log_b{b} = 1 $ for any positive base $b$.
